Solve for $x$ and $y$ using elimination. ${-3x-6y = -60}$ ${6x-5y = 18}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ ${-6x-12y = -120}$ $6x-5y = 18$ Add the top and bottom equations together. $-17y = -102$ $\dfrac{-17y}{{-17}} = \dfrac{-102}{{-17}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-3x-6y = -60}\thinspace$ to find $x$ ${-3x - 6}{(6)}{= -60}$ $-3x-36 = -60$ $-3x-36{+36} = -60{+36}$ $-3x = -24$ $\dfrac{-3x}{{-3}} = \dfrac{-24}{{-3}}$ ${x = 8}$ You can also plug ${y = 6}$ into $\thinspace {6x-5y = 18}\thinspace$ and get the same answer for $x$ : ${6x - 5}{(6)}{= 18}$ ${x = 8}$